3 papers
math.NA2026
Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers
Nilo Schwencke, Roland Maier
Physics-informed neural networks and finite element methods provide two different paradigms for the numerical approximation of partial differential equations: the former are common…
cs.LG2025
AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM
Nilo Schwencke, Cyriaque Rousselot, Alena Shilova +1
Recent works have shown that natural gradient methods can significantly outperform standard optimizers when training physics-informed neural networks (PINNs). In this paper, we ana…
cs.LG2024
ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning
Nilo Schwencke, Cyril Furtlehner
In the recent years, Physics Informed Neural Networks (PINNs) have received strong interest as a method to solve PDE driven systems, in particular for data assimilation purpose. Th…